A three phase, $50$Hz$,80$hp$,4$pole, star connected induction motor operating at rated conditions has an

efficiency of $90$ percent. The core loss, stator copper loss, and rotor copper loss are $1500,2000,$ and $1400$W$,$

respectively. Determine:

a$)$ The input power.

b$)$ Air gap power.

c$)$ Shaft speed.

d$)$ Rotational power loss.